1. Field of the Invention (Technical Field):
The present invention relates to wavelength modulation spectroscopy.
2. Background Art:
Wavelength modulation spectroscopy (WMS) is a form of optical absorption spectroscopy that allows detection of small optical absorbances of gases and, thereby, measurements of gas concentrations. The technique is effective because absorption measurements are shifted from frequencies near DC, where light sources are noisy, to high frequencies where shot-noise-limited absorption measurements are possible. This shift in detection band can improve measurement sensitivity by three to five orders of magnitude.
WMS is usually implemented with continuously tunable lasers such as diode lasers. Typically, the wavelength of the light source is modulated by a small amount about an absorption feature of the target species. The modulation frequency is f. As the light beam propagates through a sample, absorption by the target species converts some of the wavelength modulation into an amplitude modulation (AM) of the light because more light is absorbed at the absorption peak wavelength. When the light impinges onto a photodetector such as a photodiode the output signal from the detector contains AC components at the modulation frequency, f, and its higher harmonics, 2f, 3f, 4f, etc. In conventional usage, one of the AC components is selected for measurement using a phase sensitive detector such as a lock-in amplifier or a mixer. This signal processing step is known as demodulation. Usually a portion of the modulation waveform is used to generate a reference waveform (local oscillator) for the demodulator. The resulting demodulated signal is related to the optical absorbance and to the intensity of the light beam.
Detailed theory describing WMS and the relationships between the absorption lines shape and demodulated line shapes is given by Silver [J. Silver, xe2x80x9cFrequency-modulation spectroscopy for trace species detection: theory and comparison among experimental methods,xe2x80x9d Applied Optics 31, 707-717 (1992)]. In qualitative terms, the waveform produced by slowly stepping the average laser wavelength across an absorption line while demodulating at frequency nf is similar in shape to the nth derivative of the absorption line shape and is referred to as the nf signal or nf spectrum. In the limiting case where the extent (depth) of modulation is much less than the absorption line width, theory predicts that the nf spectrum is directly proportional to the exact nth derivative of the absorption line shape.
The shape of a wavelength modulation spectrum depends strongly on the ratio of the extent of the wavelength modulation to the line width of the absorption feature. Any phenomenon that changes the absorber line width, such as variations in sample pressure or, to a lesser extent, variations in sample temperature, will change the shape and peak intensities of the corresponding wavelength modulation spectrum. Changes in absorber line width can, therefore, introduce error into quantitative applications of WMS particularly where such applications are used to measure species concentrations.
A number of methods exist that can be used to apply wavelength modulation spectra for gas sensing despite changes in the absorber line width; each of these approaches, however, has some limitation. For example, Wilson [G. V. H. Wilson, xe2x80x9cModulation broadening of NMR and ESR line shapes,xe2x80x9d J. Appl. Phys. 34, 3276-3285 (1963)] shows that the exact shape of a wavelength modulation spectrum can be used to extract the absorber line width and, thereby, calculate the actual optical absorbance and the species concentration. Wilson""s method, however, requires WMS measurements that are free of noise and background artifacts (i.e., etalons) in order to obtain accurate line widths, absorbances, and species concentrations. Wilson""s numerical inversion methods do not always guarantee convergence and are subject to numerical singularities.
Goldstein et al. patented an improvement to wavelength modulation spectroscopy in which the detector signal at twice the modulation frequency (2f) is monitored while the extent of the wavelength modulation is changed [N. Goldstein, F. Bien, and L. Bernstein, xe2x80x9cGaseous Species Absorption Monitor,xe2x80x9d U.S. Pat. No. 5,026,991, issued Jun. 25, 1991; N. Goldstein, S. Adler-Golden, J. Lee, and F. Bien, xe2x80x9cMeasurement of molecular concentrations and line parameters using line-locked second harmonic spectroscopy with an AlGaAs diode laser,xe2x80x9d Appl. Opt. 31, 3409-3415 (1992)]. The response of the 2f signal as a function of extent of modulation is representative of the shape and width of the absorption line. Goldstein""s invention is simple to implement because it requires only a minor modification to standard WMS instrumentation. The most significant limitation of the invention, however, arises because lasers often respond non-linearly to applied modulation waveforms. Both the extent (depth) of modulation and the time dependence of the output wavelength may not track well the changes in the applied modulation signal. Proper implementation of the invention may require careful calibration of the response of each laser or using customized (e.g., non-sinusoidal) modulation waveforms. The nonlinearities are particularly important when relatively large wavelength excursions are needed, such as occur for detecting absorbances from samples at atmospheric or higher pressure.
Species concentrations inferred from wavelength modulation spectra can be corrected by measuring sample temperature and pressure, and using corrections calculated from basic theory or from tabulated calibrations. The computational approach can be slow, however, and requires a significant amount of computing power; tabulating a set of corrections requires a lengthy and tedious calibration. In both cases, the instrument is made more complex and more expensive by adding pressure and temperature sensors.
Other patents discussing related technology but different from the present invention include: U.S. Pat. No. 5,640,245, to Zybin et al., entitled xe2x80x9cSpectroscopic Method with Double Modulation;xe2x80x9d U.S. Pat. No. 5,636,035, to Whittaker et al., entitled xe2x80x9cMethod and Apparatus for Dual Modulation Laser Spectroscopy;xe2x80x9d U.S. Pat. No. 5,267,019, to Whittaker et al., entitled xe2x80x9cMethod and Apparatus for Reducing Fringe Interference in Laser Spectroscopy;xe2x80x9d U.S. Pat. No. 5,498,875, to Obremsky et al., entitled xe2x80x9cSignal Processing for Chemical Analysis of Samples;xe2x80x9d U.S. Pat. No. 5,637,872, to Tulip, entitled xe2x80x9cGas Detector;xe2x80x9d U.S. Pat. No. 5,448,071 to McCaul et al., entitled xe2x80x9cGas Spectroscopy;xe2x80x9d U.S. Pat. No. 5,068,864, to Javan, entitled xe2x80x9cLaser Frequency Stabilization;xe2x80x9d U.S. Pat. No. 4,990,775, to Rockwood et al., entitled xe2x80x9cResolution Improvement in an Ion Cyclotron Resonance Mass Spectrometer,xe2x80x9d and U.S. Pat. No. 4,468,773, to Seaton, entitled xe2x80x9cLaser Control Apparatus and Method.xe2x80x9d
U.S. Pat. No. 5,015,848 to Bomse et al., entitled xe2x80x9cMass Spectrometric Apparatus and Method,xe2x80x9d is related to the field of mass spectrometry, but has no relation to the present invention except for the presence of common inventors, and is included here only for the sake of completeness. Co-pending Application Ser. No. 09/005,356, to Bomse, entitled xe2x80x9cPhaseless Wavelength Modulation Spectroscopy,xe2x80x9d is perhaps most relevant to the present invention and the disclosure therein is incorporated herein by reference. It improves wavelength modulation spectroscopy by extracting information about the line width and line shape of absorption features. The information is in the form of the relative intensities of wavelength modulation spectra acquired at a plurality of demodulated harmonics. This added information can be used to improve the accuracy of gas concentration measurements or to infer physical properties of the gas such as pressure, temperature, and chemical composition.
A key difference between xe2x80x9cPhaseless Wavelength Modulation Spectroscopyxe2x80x9d and the present invention is that the phaseless method uses one heterodyne demodulation whereas the current invention uses a plurality of homodyne demodulations. In terms of practicality and usefulness, the present invention provides more accurate answers because homodyne demodulations are less noisy than are heterodyne demodulations. The homodyne approach excludes more noise by operating at narrower bandwidth. Also, homodyne demodulations operate at unit duty cycle whereas the heterodyne methodxe2x80x94which uses narrow pulses for the local oscillatorxe2x80x94acquires demodulated signal only during the pulse xe2x80x9cONxe2x80x9d period which may be just a few percent of each demodulation cycle. Regarding apparatus needed to implement the methods, the heterodyne approach requires two modulation frequencies, specified as xcexa9 and xcex4, while the current invention needs only one modulation frequency (f). Conversely, the heterodyne approach requires only one demodulation waveform and one demodulator while the current invention requires a plurality of demodulation waveforms (one for each harmonic of f) and is most efficiently implemented using a plurality of demodulators.
The present invention overcomes the limitations of the prior art by demodulating the detector output at a plurality of the harmonic frequencies, not just one, nf. Demodulation at only one frequency, nf, (as conventionally practiced) throws away absorbance information that is available at other harmonics of the modulation frequency. If, instead, the detector output is demodulated at a plurality of frequencies, each frequency being an integer multiple of the wavelength modulation frequency, f, then the resulting signals can be combined to improve the accuracy and precision of the absorbance measurement. The relative magnitudes of the demodulated signals are indicative of the absorber line shape and line width; combining the absorbance data with the line shape information improves the accuracy of the gas concentration measurement over a range of gas pressures, temperatures, and concentrations. The present invention provides a method and apparatus that improves WMS by reducing the measurement uncertainty resulting from such changes. The present invention also permits, under certain circumstances, quantitative determination of spectroscopic absorption line broadening parameters using wavelength modulation spectra.
The present invention is a wavelength modulation spectroscopy system using multiple harmonic detection of the output of the photodetector. A wavelength modulation spectroscopy system has a light source, such as a laser, wavelength modulation means operating at a frequency f, and a photodetector detecting the signal after having passed through the gas, and generating an output with frequency components f, 2f, 3f, . . . nf, where n is an integer greater than one. The present invention improves upon this spectroscopy system by adding a demodulator that demodulates a plurality of the frequency components output by the photodetector. Spectroscopic information is then extracted from the demodulated frequency components to obtain information about the absorption line shape of the gas. In order to extract spectroscopic infonmation, line center magnitudes of the demodulated frequency components are measured at selected even harmonics of the modulation frequency f. A computer or other appropriate device can be used to perform such measurements and measure the line center magnitudes. Then the absorption line shape of the gas can be calculated from the relationship of the line center magnitudes. A computer or various other devices can be used to perform the calculations. Gas concentration, gas temperature, and gas pressure can be determined from the spectroscopic information that is extracted from the demodulated frequency components. Spectroscopic information can be extracted from the full wavelength modulation spectra acquired using demodulation at a plurality of even and/or odd harmonics of the modulation frequency. The system can further be constrained to the absorption line center of a target gas and in this embodiment comprises means for measuring the magnitudes of the demodulated frequency components; means for weighting the magnitudes of the demodulated frequency components at odd harmonics of the modulation frequency, based on known properties of a spectroscopic interference; means for calculating the magnitudes of the frequency components at even harmonics of the modulation frequency, due to an interfering absorption, from the weighted magnitudes; and means for determining the characteristics of the target gas, free of interferences by adjacent absorption lines, from the results of the calculation. Means for perfroming the measurements, weighting, and performing the various calculations can include, but are not limited to, a computer.
In order to perform the demodulation, a plurality of separate demodulators can be used which correspond to the selected frequency components at which demodulation is to be performed. In one embodiment the separate demodulators are each comprised of a local oscillator generating a frequency equal to a separate one of each of the selected frequency components output by the photodetector, and a mixer for performing homodyne demodulation of the frequency component. As an alternative to the first embodiment the plurality of separate demodulators are each comprised of a local oscillator again generating a frequency equal to a separate one of each of the selected frequency components output by the photodetector, and a lock-in amplifier for performing homodyne demodulation of the frequency component.
In a second embodiment the demodulator of the system comprises an analog to digital converter to convert the output of the photodetector into digital data and a computer which performs numerical demodulation of the digital data. This system can further comprise a filter for filtering noise from the demodulated digital data. The computer can perform the numerical demodulation in one of two ways, either by fast Fourier transforms or by vector dot product operations.
In a wavelength modulation spectroscopy method comprising the steps of modulating at a frequency f and generating a photodetector output having frequency components f, 2f, 3f, . . . nf, where n is an integer greater than one, the improved method comprises the step of demodulating a plurality of the frequency components output by the photodetector. The method further adds the step of extracting spectroscopic information from the demodulated frequency components to obtain absorption line shape information. In order to extract the spectroscopic information, line center magnitudes of selected even harmonics of the demodulated frequency components are measured. Then the absorption line shape can be calculated from the relationship of the line center magnitudes. An additional step can be performed wherein gas concentration, gas temperature and gas pressure can be calculated from the spectroscopic information of the demodulated frequency components. The method is also used to determine characteristics of a target gas, free of interferences by adjacent absorption lines, by first constraining the mean modulation wavelength to the absorption line center of a target gas; second measuring the magnitudes of the demodulated frequency components; third weighting the magnitudes of the odd harmonic demodulated frequency components based on known properties of spectroscopic interference; fourth calculating the magnitudes of the even harmonic demodulated frequency components due to an interfering absorption from the weighted magnitude of the odd harmonic demodulated frequency components; and finally determining the target gas characteristics from the calculation step.
The method of demodulating is comprised of demodulating selected frequency components output from the photodetector with a plurality of separate demodulators corresponding with each of the selected frequency components. In order to perform the demodulation, a frequency is generated which is equal to a separate one of each of the selected frequency components using a local oscillator; and then homodyne demodulation is performed on each frequency component with a mixer. Alternatively, demodulating can be accomplished by generating a frequency with the local oscillator, and then performing homodyne demodulation of each frequency component with a lock-in amplifier. Another way of performing the demodulating comprises converting the photodetector output into digital data with an analog to digital converter and then numerically demodulating the digital data with a computer. Noise can then be filtered from the demodulated digital data with a filter. The computer can perform the demodulation either via fast Fourier transforms or vector dot product operations.
A primary object of the present invention is to provide means for improving the accuracy and precision of wavelength modulation spectroscopy absorption measurements.
A primary advantage of the present invention is that absorption line shapes can be determined more accurately.
Another advantage of the present invention is that various gas characteristics can be determined noninvasively.
Other objects, advantages and novel features, and further scope of applicability of the present invention will be set forth in part in the detailed description to follow, taken in conjunction with the accompanying drawings, and in part will become apparent to those skilled in the art upon examination of the following, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.